Recent progress with large-scale ab initio calculations: the CONQUEST code. While the success of density functional theory (DFT) has led to its use in a wide variety of fields such as physics, chemistry, materials science and biochemistry, it has long been recognised that conventional methods are very inefficient for large complex systems, because the memory requirements scale as N2 and the cpu requirements as N3 (where N is the number of atoms). The principles necessary to develop methods with linear scaling of the cpu and memory requirements with system size ([MATHEMATICAL SCRIPT CAPITAL O](N ) methods) have been established for more than ten years, but only recently have practical codes showing this scaling for DFT started to appear. We report recent progress in the development of the Conquest code, which performs [MATHEMATICAL SCRIPT CAPITAL O](N ) DFT calculations on parallel computers, and has a demonstrated ability to handle systems of over 10000 atoms. The code can be run at different levels of precision, ranging from empirical tight-binding, through ab initio tight-binding, to full ab initio , and techniques for calculating ionic forces in a consistent way at all levels of precision will be presented. Illustrations are given of practical Conquest calculations in the strained Ge/Si(001) system